Name:
Date:
Algebra 2
Probability Review
Review Outline

Probabilities in situations where the outcomes are equally likely.
□ Probability of a single outcome =
□ Probability of an event =
1
.
total number of outcomes
number of outcomes in the event
.
total number of outcomes
□ Sometimes counting methods (such as C, P, or !) must be used to find “the total number of
outcomes” and/or “the number of outcomes in the event.”
□ For an action having two equally-likely outcomes (such as a coin flip) done n times, the
C
probability of getting a certain outcome r-out-of-n times is n n r
2

Probabilities involving “and”, “or”, “not”
(here A and B stand for events)
□ P(not A) = 1 – P(A)
□ P(A or B) = P(A) + P(B) if A and B are mutually exclusive

Dependent and independent events
□ If events A and B are dependent (the outcome of A affects the likelihood of B):
P(A and B) = P(A) · P(B | A)
where P(B | A) means prob. of B given A
□ If events A and B are independent:
P(A and B) = P(A) · P(B)


Conditional probability in tables
Use tree diagrams to organize probabilities of multiple events
Name:
Date:
Algebra 2
Review Problems
General directions: When asked to find a probability, you may give your answer as a fraction (either
unreduced or reduced) or as a decimal rounded to 3 decimal places.
1. Lara and Sara are twins. They have one graphing calculator that they share. Each day they flip a coin
to decide who gets to take the calculator to school. Suppose that they do this for 10 days. Answer
these probability questions about what happens.
a. What is the probability that Sara gets to take the calculator exactly 7 out of the 10 times?
b. What is the probability that Sara gets to take the calculator at least 7 out of the 10 times?
c. Write a question about this situation whose answer is
1
.
1024
2. Here is some probability information about two events S and T:
□ P(S) = 0.6
□ P(S and T) = 0.15
a. Identify something that has a probability of 0.4.
b. Are events S and T mutually exclusive? Justify your answer.
c. If it’s additionally given that S and T are independent, what is P(T) ?
3. From a class which has 14 girls and 6 boys, suppose a group of 3 students is picked. What is the
probability that all 3 students picked are girls? Write your answer first as a fraction then as a decimal.
Name:
Date:
Algebra 2
4. You have a green die and a red die, each numbered from 1 through 6.
First list all the possible dice rolls. Here’s some space for that:
a. What is the probability of getting a 5 on the green die and a 1 on the red die?
b. What is the probability of getting a 5 and a 1 on the two dice?
c. What is the probability of getting 4’s on both dice?
d. What is the probability that the sum of the two dice is 9?
e. What is the probability that the sum of the two dice is either 7 or 9?
f. What is the probability that the sum of the two dice is not 4?
g. What is the probability that the number on the green die is equal to the number on the red die?
h. What is the probability that the number on the green die is greater than the number on the red die?
Name:
Date:
Algebra 2
5. A cookie jar contains 4 vanilla cookies and 9 chocolate cookies. Once a cookie is taken from the jar, it
is not put back. Suppose that a cookie is randomly taken from the jar, and then a second cookie is
taken from the jar.
a. Make a tree diagram showing the probabilities in this situation.
b. Given that the first cookie is chocolate, what is the probability that the second cookie is vanilla?
c. What is the probability that the first cookie is chocolate and the second cookie is vanilla?
d. What is the probability that the two cookies are of the same kind?
e. What is the probability that the two cookies are of different kinds?
f. Now suppose that five cookies were taken from the jar, one after the other. What is the probability
that all of them are chocolate?
g. Again supposing that five cookies were taken from the jar, what is the probability that all of them
are vanilla?
Name:
Date:
Algebra 2
6. In a survey of 1000 college students, the table below gives information on how many students were
feeling stressed or not, and how many dropped out of college or not.
Dropped out
Graduated
Total
Stressed
30
570
600
Not stressed
8
392
400
Total
38
962
1000
a. What is the probability that a student drops out of this college?
b. If a student drops out, what is the probability that he or she reported being stressed?
c. Given that the selected student was feeling stressed, what is the probability that he or she
graduated?
Name:
Date:
Algebra 2
Probability Review Answers
C7
120
b. 120+45+10+1=176, answer 176/1024
=
10
1024
2
c. prob. that Sara takes the calculator all 10 days (OR: none of the 10 days)
1. a.
10
2. a. P(not S)
b. No. If they were mutually exclusive, then P(S and T) would be 0.
c. P(S and T) = P(S)  P(T)  0.15 = 0.6  P(T)  P(T) = 0.25.
3.
C3
» 0.319
20 C 3
14
4. a. 1/36
b. 2/36
c. 1/36 d. 4/36
e. 10/36
f. 33/36
g. 6/36
5. a. probabilities should be: 4/13, 9/13; 3/12, 9/12, 4/12, 8/12
15120
b. 4/12 c. 36/156 d. 84/156 e. 72/156 f. 139 × 128 × 117 × 106 × 59 = 154440
6. a.
38
1000
b.
30
38
c.
570
600
h. 15/36
g. 0